{"id":2884,"date":"2025-08-24T23:28:21","date_gmt":"2025-08-24T14:28:21","guid":{"rendered":"https:\/\/math-friend.com\/?p=2884"},"modified":"2025-08-24T23:28:23","modified_gmt":"2025-08-24T14:28:23","slug":"%e3%80%90%e5%a4%a7%e9%98%aa%e5%a4%a7%e5%ad%a6%e5%85%a5%e8%a9%a6%e3%80%91%e4%b8%89%e8%a7%92%e5%bd%a2%e3%81%ae%e8%a7%92%e5%ba%a6%e6%9d%a1%e4%bb%b6%e3%81%8b%e3%82%89%e8%be%ba%e3%81%ae%e4%b8%8d%e7%ad%89","status":"publish","type":"post","link":"https:\/\/math-friend.com\/?p=2884","title":{"rendered":"\u3010\u5927\u962a\u5927\u5b66\u5165\u8a66\u3011\u4e09\u89d2\u5f62\u306e\u89d2\u5ea6\u6761\u4ef6\u304b\u3089\u8fba\u306e\u4e0d\u7b49\u5f0f\u3092\u5c0e\u304f\u554f\u984c(2020)"},"content":{"rendered":"\n

\u4eca\u56de\u306f\u3053\u3061\u3089\u306e\u554f\u984c\u3092\u89e3\u3044\u3066\u3044\u304d\u307e\u3059.<\/p>\n\n\n\n

\\(\\triangle{\\mathrm{ABC}}\\)\u306b\u304a\u3044\u3066, \\(\\angle{\\mathrm{ACB}}=3\\angle{\\mathrm{ABC}}\\)\u3067\u3042\u308b\u3068\u304d, \\(\\mathrm{AB}<3\\mathrm{CA}\\)\u3092\u793a\u305b.
(2020 \u5927\u962a\u5927\u5b66 \u6587\u7cfb [3])<\/span><\/p>\n\n\n\n

\u305d\u308c\u3067\u306f\u89e3\u3044\u3066\u3044\u304d\u307e\u3057\u3087\u3046.<\/p>\n\n\n\n

\n

\\(\\angle{\\mathrm{ABC}}=\\theta\\)\u3068\u304a\u304f\u3068, \\(\\angle{\\mathrm{ACB}}=3\\theta\\)\u3067\u3042\u308a, \u6b63\u5f26\u5b9a\u7406\u304b\u3089,$$
\\frac{\\mathrm{CA}}{\\sin{\\theta}}=\\frac{\\mathrm{AB}}{\\sin{3\\theta}}
$$\u3067\u3042\u308a,$$
\\mathrm{AB}=\\frac{\\sin{3\\theta}}{\\sin{\\theta}}\\mathrm{CA}
$$\u3067\u3042\u308b. \u3053\u3053\u3067,$$
\\begin{align}
\\sin{3\\theta}&=\\sin{(2\\theta+\\theta)}\\\\[1.5ex]
&=sin{2\\theta}\\cos{\\theta}+\\cos{2\\theta}\\sin{\\theta}\\\\[1.5ex]
&=2\\sin{\\theta}\\cos^2{\\theta}+(1-2\\sin^2{\\theta})\\sin{\\theta}\\\\[1.5ex]
&=2\\sin{\\theta}(1-\\sin^2{\\theta})+(1-2\\sin^2{\\theta})\\sin{\\theta}\\\\[1.5ex]
&=3\\sin{\\theta}-4\\sin^3{\\theta}
\\end{align}
$$\u3068\u306a\u308b\u304b\u3089, \\(4\\sin^2{\\theta}>0\\)\u306b\u6ce8\u610f\u3057\u3066,$$
\\begin{align}
\\mathrm{AB}&=\\frac{\\sin{3\\theta}}{\\sin{\\theta}}\\mathrm{CA}\\\\[1.5ex]
&=(3-4\\sin^2{\\theta})\\mathrm{CA}<3\\mathrm{CA}
\\end{align}
$$\u3068\u306a\u308a, \\(\\mathrm{AB}<3\\mathrm{CA}\\)\u304c\u793a\u3055\u308c\u305f.<\/p>\n<\/div><\/div>\n\n\n\n

youtube\u3067\u3082\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059.<\/p>\n\n\n\n